Standardization of Gram Matrix for Improved 3D Neural Style Transfer

Neural Style Transfer based on convolutional neural networks has produced visually appealing results for image and video data in the recent years where e.g. the content of a photo and the style of a painting are merged to a novel piece of digital art. In practical engineering development, we utilize 3D objects as standard for optimizing digital shapes. Since these objects can be represented as binary 3D voxel representation, we propose to extend the Neural Style Transfer method to 3D geometries in analogy to 2D pixel representations. In a series of experiments, we first evaluate traditional Neural Style Transfer on 2D binary monochromatic images. We show that this method produces reasonable results on binary images lacking color information and even improve them by introducing a standardized Gram matrix based loss function for style. For an application of Neural Style Transfer on 3D voxel primitives, we trained several classifier networks demonstrating the importance of a meaningful convolutional network architecture. The standardization of the Gram matrix again strongly contributes to visually improved, less noisy results. We conclude that Neural Style Transfer extended by a standardization of the Gram matrix is a promising approach for generating novel 3D voxelized objects and expect future improvements with increasing graphics memory availability for finer object resolutions.